How do you multiply #(15sqrt( 8x^16)) /( 5 sqrt( 2x^4))#?

1 Answer
MeneerNask
May 2, 2015

We start by taking all squares from under the root.

Since #8=2*2*2=2*2^2# and #x^16=(x^8)^2#
And #x^4=(x^2)^2#

We can take out these squares (unsquared of course), and in both cases only a single #2# will be left under the root:

#=(15*2*x^4sqrt2)/(5*x^2sqrt2)=(30*x^2*x^2*sqrt2)/(5*x^2*sqrt2)#

Now we can cancel out the #x^2# and the #sqrt2#:

#=(30*x^2)/5=6x^2#

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